The SlugMath Wiki is under heavy development!
Def/Inverse function
From SlugmathWiki
Definition of Inverse function: Suppose that $X$ and $Y$ are sets, and $f \colon X \rightarrow Y$ is a function. Suppose that $g \colon Y \rightarrow X$ is another function. There are three notions of "inverse function", defined as follows:
- We say that $g$ is a left inverse of $f$ if $g \circ f = Id_X$ (the identity function from $X$ to itself).
- We say that $g$ is a right inverse of $f$ if $f \circ g = Id_Y$ (the identity function from $Y$ to itself).
- We say that $g$ is a two-sided inverse (or just inverse) of $f$ if $g$ is a left and right inverse.
Logical Connections
This definition logically relies on the following definitions and statements: Def/Function, Def/Identity function
The following statements and definitions logically rely on the material of this page: State/Injective functions have left inverses, and State/Surjective functions have right inverses
To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Functions
